2 Answers
2

Unfortunately, this is a huge question. So, I'll provide a generic overview answer from a few sources.

First, here is the Wikipedia article describing Emerging churches (the Emergent Movement). It covers a lot of ground.

A simpler overview of their principles can be found in Emerging Churches: Creating Christian Community in Postmodern Cultures by Eddie Gibbs and Ryan Bolger (Baker Academic, 2005)

Emerging churches are communities that practice the way of Jesus
within postmodern cultures. This definition encompasses nine
practices. Emerging churches (1) identify with the life of Jesus, (2)
transform the secular realm, and (3) live highly communal lives.
Because of these three activities, they (4) welcome the stranger, (5)
serve with generosity, (6) participate as producers, (7) create as
created beings, (8) lead as a body, and (9) take part in spiritual
activities.

Finally, there's an interesting Christianity Today article about it here.

Trying to give much more detail than that would lead to a book deal.

As far as who identifies themselves with that movement, it seems that they do have community that clearly defines themselves as "emergent". (here).

+1 for the Christianity Today link. "Emergent" seems by its nature a bit hard to pin down from a traditional evangelical perspective, but that article helps me get a feel for it. I wonder if the movement is trying so hard to avoid what they see as a problem, that they are minimizing and maybe even discarding what should be held most dear.
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jimreedAug 25 '11 at 16:16

Richard's answer is all true, but I'd venture to say that nearly all Christians would agree with items 1-9, and so it isn't very helpful to distinguish what is unique about the movement.
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Patrick SzalapskiAug 26 '13 at 14:12

DeWaay, in The Emergent Church: Undefining Christianity, (on Amazon but in stock on CICstore) asserts that Emergents believe in a hopeful view that "the kingdom of God is emerging through the processes of history because God is the future, drawing everything into Himself" (DeWaay 11). See DeWaay's book for that case, but I think this is a fair assessment.

How this looks in a few details:

Emergents usually reject final judgment, preferring to think God will "save" everyone in a tangible paradise here on earth.

Their mission is not first to spread the saving Gospel message of Jesus Christ to individuals, but instead to do good in society and make life better to all.

They want to create coherent meaning specific to a church or other community, rather than seeking objective meaning and absolute truth.

Truth and meaning are experienced, rather than known.

Conversely, experiences are more important than doctrine.

They seek spiritual growth in many various ways, usually rejecting that the biblical means of grace (Bible teachings, prayer, fellowship, the Lord's Supper) are paramount.

Many even go so far as to reject basic logic as useless: they won't acknowledge the self-evident basic logic laws that all people follow every day, that A is A, A is not non-A, and A and non-A cannot be both true.

Some identify themselves as Emergent or emerging; many followers or proponents of emergent thought do not identify themselves as such. One such self-identifying source is the Emergent Village.

I do not think it should be regarded as a catch-all term.

Emergents will try to avoid any straight, direct answers, and they may object to my broad strokes here. Their beliefs also vary among each other, of course.